A right triangle has 1 leg that is 2" longer than the other leg. the length of the hypotenuse is sqrt 130" Find lengths of legs

Question

0=2x^+4x-126

Answer 1

short leg --- x
longer leg -- x+2

x^2 + (x+2)^2 = (√136)^2
x^2 + x^2 + 4x + 4 = 136
2x^2 + 4x - 132 = 0
x^2 + 2x - 66 = 0
I will complete the square:
x^2 + 2x + .... = 66 + ...
x^2 + 2x + 1 = 66 + 1
(x+1)^2 = 67
x+1 = ±√67
x = -1 + √67 , since x > 0

so the short leg = √67 - 1 , and the longer is √67+1

Answer 2

Factor to solve for x, which cannot be negative.

126 = 3 * 2 * 7 * 3 = 18 * -7

Work it from there.

Answer 3

In contrast to Reiny, I factor to get
(2x+18)(x-7) = 0

Since the distance cannot be negative:

x = 7

x + 2 = 9

Answer 4

thank you for all the help

Answer 5

Where does the 126 come from?
the original question had √136

Answer 6

I saw 130, which minus 4 = 126.